It's a horror adventure game, played from a first person perspective. The story starts with when the protagonist, Daniel, wakes up in a seemingly deserted castle and has no memory of anything except his name. So you have to explore further to find out what the hell's going on.
Now, although the amnesia thing is one of the biggest clichés around, the story that starts unraveling is actually really interesting. It slowly gets pieced together as you rummage through the castle, having flashbacks to previous conversations and finding various notes and pages from Daniel's diary and whatnot.
But as fascinating as all that is, the main thing about the game is that it's one of the scariest goddamn horror games ever. Seriously.

See, Daniel is not alone in the castle, ohhh no. There are monsters lurking about. They are relatively rare, but when they do appear, holy hell. The thing is that while the game is in first person, like a shooter, You have absolutely no weapons whatsoever. No way at all to fight back. So when a monster does appear you either run and hide, or die horribly.
And even when monsters aren't breathing down your neck, the atmosphere in the game is fantastically creepy. All manner of freaky occurrences and the phenomenally eerie soundscape keep you on your toes all the time. Not to mention the darkness, which is omnipresent.

Ohhh, the darkness. You do have a lantern, but it burns oil at an alarming rate, and refills aren't awfully abundant. You can also light up torches and candles in the environment, but the tinderboxes used for that are also limited. Then there's also the thing that light isn't actually good for hiding.
On the other hand light is good for Daniel's rather shaky sanity, whereas being in darkness, experiencing unsettling things and looking at monsters eats away at it. And when Daniel's sanity drops low enough, it starts affecting visibility and controls, and makes hiding more difficult. And you can only regain your wits by making progress in the game.

So all in all, I heartily recommend Amnesia: The Dark Descent for anyone who agrees that it's fun to be scared shitless by a game.

And The Lord said unto John: 'Come forth and receive eternal life'.
But John came fifth, and won a toaster.

That video was actually what made me get the game in the first place. Only watched a bit of the beginning first, then I decided I want the game myself so I didn't watch the video further. When I got past that part in the game, I watched the rest of the video. It's hysterical once you've been through it and can relate to the guy.

My reactions haven't been quite as strong as his, but still it has made me shit a few bricks. Awesome game.

And The Lord said unto John: 'Come forth and receive eternal life'.
But John came fifth, and won a toaster.

Finally got to playing Amnesia. I think I'm about 2 hours in the game now, and this is my first impression after that first session.

I like it quite a lot ! The atmosphere and the buildup of suspence is just perfect ! So far I explored thoroughly and I tend to move real slow, because I can't help but being aware of the constant threat that "something scary is gonna happen real fucking soon". I'm the type of gamer who wants to get familiar with every nook and cranny before moving on anyway, and this game really rewards that type of approach. I got spooked by the various visual and audio effects (which are really contributing to the ever building tension !) and ran into the occasional horrifying looking creature. When that happened, I simply fled from it to some unlit corner, hoping it would just lose track of me and abandon his pursuit. Up till now this tactic seems to be enough for me to progress further into the castle. Except for the chase scene through the flooded cellar, with the invisible monster right fucking there behind me ... that was fucking memorable and really worked on my nerves, shit !

I'm quitting now, because I'm getting tired. And when I get tired, even one of my own farts is capable of giving me the creeps, let alone a survival horror game in which you have absolutely NOTHING at all to fight back !

I'm really glad I picked Amnesia up, it has been an awesome and sometimes terrifying journey so far.